Meeting Details

ABSTRACT: For arbitrary smooth initial data, the solution of a hyperbolic PDE can exhibit wild behavior.
However, using differential geometric methods, sometimes one can prove that "most" solutions
are in fact quite nice. In other words, if we remove a (topologically small) set of initial data leading to pathological behavior,
all the remaining solutions have a high degree of regularity.
For example, the solution to a conservation law with smooth initial data can develop countably many shocks.
But for an open dense set of C^2 initial data only finitely many shocks appear, located along smooth curves in the t - x plane,
with finitely many intersection points.
This talk will review some basic ideas and techniques in the generic theory of PDEs,
and discuss some possible future applications.